Question: Simplify the following expression: $r = \dfrac{-90y - 40}{-60y + 90}$ You can assume $y \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-90y - 40 = - (2\cdot3\cdot3\cdot5 \cdot y) - (2\cdot2\cdot2\cdot5)$ The denominator can be factored: $-60y + 90 = - (2\cdot2\cdot3\cdot5 \cdot y) + (2\cdot3\cdot3\cdot5)$ The greatest common factor of all the terms is $10$ Factoring out $10$ gives us: $r = \dfrac{(10)(-9y - 4)}{(10)(-6y + 9)}$ Dividing both the numerator and denominator by $10$ gives: $r = \dfrac{-9y - 4}{-6y + 9}$